Computational Techniques of Rotor Dynamics with the Finite Element Method

For more than a century, we have had a firm grasp on rotor dynamics involving rigid bodies with regular shapes, such as cylinders and shafts. However, to achieve an equally solid understanding of the rotational behavior of flexible bodies—especially those with irregular shapes, such as propeller and turbine blades—we require more modern tools and methods.
Computational Techniques of Rotor Dynamics with the Finite Element Method explores the application of practical finite element method (FEM)-based computational techniques and state-of-the-art engineering software. These are used to simulate behavior of rotational structures that enable the function of various types of machinery—from generators and wind turbines to airplane engines and propellers.
The book’s first section focuses on the theoretical foundation of rotor dynamics, and the second concentrates on the engineering analysis of rotating structures. The authors explain techniques used in the modeling and computation of the forces involved in the rotational phenomenon. They then demonstrate how to interpret and apply the results to improve fidelity and performance.
Coverage includes:


Use of FEM to achieve the most accurate computational simulation of all gyroscopic forces occurring in rotational structures




Details of highly efficient and accurate computational and numerical techniques for dynamic simulations




Interpretation of computational results, which is instrumental to developing stable rotating machinery




Practical application examples of rotational structures’ dynamic response to external and internal excitations


An FEM case study that illustrates the computational complexities associated with modeling and computation of forces of rotor dynamics




Assessment of propellers and turbines that are critical to the transportation and energy industries


Useful to practicing engineers and graduate-level students alike, this self-contained volume also serves as an invaluable reference for researchers and instructors in this field.

Arne Vollan studied aeronautical engineering at the Technical University of Trondheim (Norway) and Aachen (Germany), and holds the degree Diplom Ingenieur. He was employed by several aeronautical companies such as VFW-Fokker (now Airbus), Helicopter Technik Muenchen, Dornier, Nationaal Lucht- en Ruimtevaartlaboratorium, and Pilatus Aircraft as a dynamic and aeroelastic specialist. He was also a consultant and developed programs for the analysis of rotating structures like wind turbines and propellers. Since 2002 he has been working at AeroFEM GmbH in Switzerland on rotor dynamics and the aeroelasticity of aircraft and large wind turbines.

Louis Komzsik is a graduate of the Technical University of Budapest with an engineering degree and the Eötvös University of Sciences in Budapest with a mathematics degree, and he holds a Doctorate from the Technical University of Budapest, Hungary. He was employed by the Hungarian Shipyards from 1972 to 1980 and worked at the McDonnell-Douglas Corporation in 1981 and 1982. He was the chief numerical analyst at the MacNeal-Schwendler (now MSC Software) Corporation for two decades. Since 2003 he has been the chief numerical analyst at Siemens PLM Software. For the past 30 years he has been the architect of the modern numerical methods of NASTRAN, the world’s leading finite element analysis tool in structural engineering.

Part I: Theoretical Foundation of Rotor Dynamics

Introduction to Rotational Physics
Fixed Coordinate System
Rotating Coordinate System
Forces in the Rotating System
Transformation between Coordinate Systems
Kinetic Energy Due to Translational Displacement
Kinetic Energy Due to Rotational Displacement
Equation of Motion in Rotating Coordinate System
Equation of Motion in the Fixed Coordinate System

Coupled Solution Formulations
Matrix Formulation of Lagrange’s Equations
Coupling Nodal Translations to the Stationary Part
Simultaneous Coupling of Translations and Rotations
Full Coupling of the Stationary and Rotating Parts
Time-Dependent Terms of Equations

Finite Element Analysis of Rotating Structures
Potential Energy of Structure
Dissipative Forces
Non-dissipative Forces
Finite Element Equation Assembly
Coupled Equilibrium Equation Assembly
Analysis Equilibrium Equations

Computational Solution Techniques
Direct Time Domain Solution of the Equilibrium Equation
Direct Frequency Domain Solution
Direct Free Vibration Solution
Modal Solution Technique
Static Condensation
Dynamic Reduction

Numerical Solution Techniques
The Lanczos Method
Orthogonal Factorization
The Block Lanczos Method
Solution of Periodic Equations


Part II: Engineering Analysis of Rotating Structures

Resonances and Instabilities
Analysis Type vs. Modeling Approach
Resonances and Instabilities
Critical Speed of Rotating Mass
The Laval Rotor
Influence of Damping
Unsymmetric Effects of Bearing and Rotor
A Rotating Tube
Rotating Model with Flexible Arms
The Ground Resonance

Dynamic Response Analysis
Frequency Response without Rotation
Frequency Response with Rotation
Transient Response without Rotation
Transient Response with Rotation

A Finite Element Case Study
Turbine Wheel with Shaft and Blades
Engineering Analysis
Computational Statistics
The Journal Bearing
Active External Loads

Analysis of Aircraft Propellers
A Propeller Blade
Quasi-steady Aerodynamics of Blade
Unsteady Aerodynamics of Blade
Propeller with Four Blades

Analysis of Wind Turbines
An Example Wind Turbine
Modeling and Analysis of Wind Turbine Blade
Wind Turbine with Three Blades
Response Analysis of Wind Turbines
Horizontal Axis Wind Turbines with Two Blades